You should be okay for getting one but you won't be able to order one until they become available for 'general sale' (i.e. open to the public).
You'll need to register here to be able to buy one: http://eticketing.Everton.../Home/home.aspx
However, there is a way to get them before they go on general sale and that is by buying an 'Evertonia' membership. This allows you to buy the tickets three days before they go on public release. They cost £19.99 but come with a £5 off voucher for the game.
Although, before paying USD$50 for the chance to buy tickets. It may be worth emailing corporatesales@evertonfc.com and explaining that you're coming over from US and that you're interested in buying two tickets for the Newcastle game. With corporate sales, you get a drink and a meal (that's if your making it an 'occasion'). If you want a 'normal' ticket, email boxoffice@evertonfc.com and explain the same thing. They may be able to help you out, from what I've heard the club are usually very supportive of international fans.
The end of season awards take place on May 10th, depending upon your budget, it may be worth looking into getting tickets for that, he'll meet the players and drink champagne.